On The Euclidean Algorithm: Rhythm Without Recursion
History and Overview
2022-06-28 v1 Number Theory
Abstract
A modified form of Euclid's algorithm has gained popularity among musical composers following Toussaint's 2005 survey of so-called Euclidean rhythms in world music. We offer a method to easily calculate Euclid's algorithm by hand as a modification of Bresenham's line-drawing algorithm. Notably, this modified algorithm is a non-recursive matrix construction, using only modular arithmetic and combinatorics. This construction does not outperform the traditional divide-with-remainder method; it is presented for combinatorial interest and ease of hand computation.
Cite
@article{arxiv.2206.12421,
title = {On The Euclidean Algorithm: Rhythm Without Recursion},
author = {Thomas Morrill},
journal= {arXiv preprint arXiv:2206.12421},
year = {2022}
}